{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import seaborn as sb # pretty plots\n",
    "\n",
    "import scipy as scp # optimization, probability density functions and special functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "plt.rcParams['figure.figsize'] = (16.0, 8.0) # big figures on my computer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from __future__ import print_function\n",
    "from ipywidgets import interact, interactive, fixed, interact_manual\n",
    "import ipywidgets as widgets"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Evaluation of classifiers\n",
    "\n",
    "Let's define a simple threshold-based classifier and compute:\n",
    "- Its ROC curve\n",
    "- Its Precision-Recall curve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def gen_data(n_a = 500, n_b = 500, difficulty = 1):\n",
    "    x = np.zeros(shape = [n_a + n_b])\n",
    "    y = np.zeros(shape = [n_a + n_b])\n",
    "    \n",
    "    x[0:n_a] = np.random.randn(n_a) * difficulty\n",
    "    y[0:n_a] = 0\n",
    "    \n",
    "    x[n_a:(n_a+n_b)] = 4 + (np.random.gamma(shape = 4, scale = 1, size = [n_b]) - 4 ) * difficulty\n",
    "    y[n_a:(n_a+n_b)] = 1\n",
    "    \n",
    "    return x,y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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gO2ET/nffBQA7gn0Jm2E7YRMOH3YMyybYn7CF5hYYVtVz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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7989b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "diff = 1\n",
    "\n",
    "x,y = gen_data(difficulty = diff)\n",
    "\n",
    "plt.hist( x[y==0], bins = 50, label = \"Class 0\")\n",
    "plt.hist( x[y==1], bins = 50, label = \"Class 1\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def classifier(x, th = 1):\n",
    "    return 1. * ( x >= th )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.98399999999999999,\n",
       " 0.84199999999999997,\n",
       " 0.91300000000000003,\n",
       " 0.86164623467600698)"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def classification_stats(y, y_hat):\n",
    "    sensitivity = np.sum( (y == y_hat) * (y == 1) ) / np.sum( y == 1 )\n",
    "    specificity = np.sum( (y == y_hat) * (y == 0) ) / np.sum( y == 0 )\n",
    "    miss_rate   = np.mean( (y == y_hat))\n",
    "    \n",
    "    precision   = np.sum( (y == y_hat) * (y_hat == 1) ) / np.sum( y_hat == 1 )\n",
    "    \n",
    "    return sensitivity, specificity, miss_rate, precision\n",
    "    \n",
    "diff = 1\n",
    "\n",
    "x,y = gen_data(difficulty = diff)\n",
    "y_hat = classifier(x, 1)\n",
    "\n",
    "classification_stats(y, y_hat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Program Files\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:2: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n",
      "  from ipykernel import kernelapp as app\n",
      "C:\\Program Files\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:3: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n",
      "  app.launch_new_instance()\n",
      "C:\\Program Files\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:5: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n",
      "C:\\Program Files\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:6: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n",
      "C:\\Program Files\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:8: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n",
      "C:\\Program Files\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:9: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n"
     ]
    },
    {
     "data": {
      "image/png": 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QAAAMunBYeustacOGzhj48sv2gSHDh0vTpknz5ll67LE27dhhFD0QGrndbfyl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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xbf2f5f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def ROC(x,y, th_array = np.linspace(-20,20,101) ):\n",
    "    roc_x = np.zeros_like(th_array)\n",
    "    roc_y = np.zeros_like(th_array)\n",
    "    \n",
    "    for i in range(len(th_array)):\n",
    "        th = th_array[i]\n",
    "        \n",
    "        y_hat = classifier(x,th)\n",
    "        \n",
    "        sensitivity, specificity, miss_rate, precision = classification_stats(y, y_hat)\n",
    "        \n",
    "        roc_x[i] = 1 - specificity\n",
    "        roc_y[i] = sensitivity\n",
    "        \n",
    "    plt.plot(roc_x, roc_y, '-o')\n",
    "    plt.plot(roc_x, roc_x, 'k--')\n",
    "\n",
    "for diff in [2]: #[0.05, 1,2,3,4,5]:\n",
    "    for prop_0 in [0.5]: #[0.5, 0.95]:\n",
    "        n_a = np.round(10**3 * prop_0)\n",
    "        n_b = np.round(10**3 * (1-prop_0))\n",
    "        x,y = gen_data(n_a, n_b, difficulty = diff)\n",
    "        ROC(x,y)\n",
    "\n",
    "    \n",
    "plt.xlim([-0.1,1.1])\n",
    "plt.ylim([-0.1,1.1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Program Files\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:2: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n",
      "  from ipykernel import kernelapp as app\n",
      "C:\\Program Files\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:3: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n",
      "  app.launch_new_instance()\n",
      "C:\\Program Files\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:5: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n",
      "C:\\Program Files\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:6: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n",
      "C:\\Program Files\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:8: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n",
      "C:\\Program Files\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:9: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n"
     ]
    },
    {
     "data": {
      "image/png": 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vGDlyBitWTCGdLiEOBgEC6XQJtbWTmTbtmgx+AkmSpF1jOChJkiRRv0/hNdfA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\npyR5NMlbt3PcZUk+leTmHr4TAAAAANjBuoqDpZS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o4e85h6Tze83HkxyU5M1Jfi/Jx6Zk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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xbeb6550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def prec_recall(x,y, th_array = np.linspace(-20,20,101) ):\n",
    "    curve_x = np.zeros_like(th_array)\n",
    "    curve_y = np.zeros_like(th_array)\n",
    "    \n",
    "    for i in range(len(th_array)):\n",
    "        th = th_array[i]\n",
    "        \n",
    "        y_hat = classifier(x,th)\n",
    "        \n",
    "        sensitivity, specificity, miss_rate, precision = classification_stats(y, y_hat)\n",
    "        \n",
    "        curve_x[i] = sensitivity\n",
    "        curve_y[i] = precision \n",
    "        \n",
    "    plt.plot(curve_x, curve_y, '-o')\n",
    "    plt.plot(curve_x, np.ones_like(curve_x) * np.mean(y), 'k--')\n",
    "    \n",
    "for diff in [2]: #[0.05, 1,2,3,4,5]:\n",
    "    for prop_0 in [0.5]: #[0.5, 0.95]:\n",
    "        n_a = np.round(10**3 * prop_0)\n",
    "        n_b = np.round(10**3 * (1-prop_0))\n",
    "        x,y = gen_data(n_a, n_b, difficulty = diff)\n",
    "        prec_recall(x,y)\n",
    "\n",
    "    \n",
    "plt.xlim([-0.1,1.1])\n",
    "plt.ylim([-0.1,1.1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "> <ipython-input-40-89c31e6ee431>(8)gen_data()\n",
      "-> x[n_a:(n_a+n_b)] = 4 + (np.random.gamma(shape = 4, scale = 1, size = [n_b]) - 4 ) * difficulty\n",
      "(Pdb) n_a\n",
      "800.0\n",
      "(Pdb) n_b\n",
      "199.99999999999994\n",
      "(Pdb) q\n"
     ]
    }
   ],
   "source": [
    "import pdb\n",
    "pdb.pm()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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